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8ac2d450
Найдите значение выражения
4
3
⋅
6
7
⋅
21
4\sqrt{3}\cdot 6\sqrt{7}\cdot \sqrt{21}
4
3
⋅
6
7
⋅
21
Ответ:
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Решение
4
3
⋅
6
7
⋅
21
=
4
⋅
3
⋅
6
⋅
7
⋅
3
⋅
7
=
4
⋅
6
⋅
3
⋅
7
⋅
3
⋅
7
=
24
⋅
(
3
⋅
3
)
⋅
(
7
⋅
7
)
=
24
⋅
3
⋅
7
=
504
\begin{aligned}
{}& 4\sqrt{3}\cdot 6\sqrt{7}\cdot \sqrt{21} = 4\cdot \sqrt{3}\cdot 6\cdot \sqrt{7}\cdot \sqrt{3\cdot 7} = \\
& 4\cdot 6\cdot \sqrt{3}\cdot \sqrt{7}\cdot \sqrt{3}\cdot \sqrt{7} = \\
& 24\cdot (\sqrt{3}\cdot\sqrt{3})\cdot (\sqrt{7}\cdot\sqrt{7}) = \\
& 24\cdot 3\cdot 7 = 504
\end{aligned}
4
3
⋅
6
7
⋅
21
=
4
⋅
3
⋅
6
⋅
7
⋅
3
⋅
7
=
4
⋅
6
⋅
3
⋅
7
⋅
3
⋅
7
=
24
⋅
(
3
⋅
3
)
⋅
(
7
⋅
7
)
=
24
⋅
3
⋅
7
=
504
Ответ:
504
504
504
.
